Abstract
The theory of similarity transformations, which is the main part of square matrix theory, deals with numerous classes of special matrices. Accordingly, there are many ways to describe such classes. In most cases, the fact that a matrix belongs to a required class can be checked by a rational calculation, that is, by a finite algorithm that uses arithmetic operations only. Congruence transformations occupy a more modest place in matrix theory compared to similarities. However, in this branch of theory, there also are numerous classes of special matrices. In this paper, we use several examples to discuss whether it is possible to verify the fact that a matrix belongs to a required congruence class via a rational calculation.
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REFERENCES
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Ikramov, K.D. On Rational Algorithms for Recognition of Belonging to Congruence Classes. MoscowUniv.Comput.Math.Cybern. 47, 141–144 (2023). https://doi.org/10.3103/S0278641923020048
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DOI: https://doi.org/10.3103/S0278641923020048